What is the integral of ((cos(sqrt(x))))/(sqrt(x)) ?

The integral of ((cos(sqrt(x))))/(sqrt(x)) is 2sin(sqrt(x))+C

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integral of ((cos(sqrt(x))))/(sqrt(x))

\int \frac{( cos ( x ) )}{x} d x

2 sin (x) + C

Solution steps

\int \frac{cos ( x )}{x} d x

Apply u-substitution

: \int 2 cos (u) d u

= \int 2 cos (u) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 2 sin (u)

Substitute back

u = x

= 2 sin (x)

Add a constant to the solution

= 2 sin (x) + C

\int \frac{x}{( 9 - x ^{2} ) ^{2}} d x

x \to 11 lim (\frac{3 x - 33}{11 x - 11})

e^{- s} (\frac{1}{s ^{2}} - \frac{1}{s})

\frac{d y}{d x}, 5 e^{x y} - 4 x = y + 30.9

\frac{d}{d x} ((8 x)^{\frac{1}{2}})

What is the integral of ((cos(sqrt(x))))/(sqrt(x)) ?
The integral of ((cos(sqrt(x))))/(sqrt(x)) is 2sin(sqrt(x))+C